If ${\tan ^{ - 1}}x - {\tan ^{ - 1}}y = {\tan ^{ - 1}}A,$ then $A$ is equal to:

If $\theta = \sec^{-1}(\cosh u)$,then $u =$

The solution of $\tan ^{-1} x+2 \cot ^{-1} x=\frac{2 \pi}{3}$ is

Considering only the principal values of inverse trigonometric functions,the number of positive real values of $x$ satisfying $\tan ^{-1}(x)+\tan ^{-1}(2 x)=\frac{\pi}{4}$ is:

If $\sin^{-1}(1 - x) - 2\sin^{-1}x = \pi/2$,then $x$ equals:

The value of $\tan \left(\frac{\pi}{4}+\frac{1}{2} \cos ^{-1}\left(\frac{a}{b}\right)\right)+\tan \left(\frac{\pi}{4}-\frac{1}{2} \cos ^{-1}\left(\frac{a}{b}\right)\right)$ is